**7. Final Remarks**

Investigations were made on HT properties and the entropy formation of P-ENF using a stretchable sheet. The single-phase method was employed to construct a computational model. Various physical parameters extract the results with the variations in energy, entropy, and velocity. The impacts of the thermal conductivity parameter *<sup>υ</sup>*<sup>∗</sup>, the thermal radiative parameter *N<sup>π</sup>*, Prandtl–Eyring parameters *τ*<sup>∗</sup> and *ς*<sup>∗</sup>, the velocity slip parameter *Λπ*, Biot number *B<sup>π</sup>*, *BΓ*, and *R<sup>π</sup>*, as well as nanomolecular size *φ* and porous media parameter *Fπ* were examined in the study. Some of the main developments from the study were: The increment in the size of nanoparticles resulted in amplifying the heat transfer rate in engine oil. According to the analysis, copper nanofluid is a better heat conductor than aluminium oxide nanofluid. Increasing the porous media parameter *F<sup>π</sup>*, thermal radiative flow *N<sup>π</sup>*, size parameter *φ*, and Brinkman number *BΓ*, the entropy was also enhanced. However, entropy was diminished with a rise in velocity slip parameter *Λπ*. An increment in the porous media parameter resulted in increasing the velocity. At the same time, it decreased with the nanoparticles' size augmentation.

The results obtained from the present study can help future researchers improve the heat effect. Heating systems can be formed using various non-Newtonian nanofluids, including Casson, Carreau, second-grade, Maxwell, micropolar, etc. The efficacy of timedependent porosity and viscosity along with magneto slip flow can be represented by expanding the study.

**Author Contributions:** Conceptualization, N.H.A.-H. and M.R.S.; methodology, N.H.A.-H.; software, K.H.A. and A.A.A.; validation, M.A.E.; formal analysis, K.A.A. and M.A.E.; investigation, resources, K.H.A.; visualization, A.A.A. and K.H.A.; data curation, K.A.A., writing—original draft preparation, A.M.A.; writing—review and editing, M.R.S. and K.A.A.; supervision, N.H.A.-H. and M.R.S.; project

administration, A.A.A. and N.H.A.-H.; funding acquisition, M.R.S. and N.H.A.-H. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number "IFPNC-006-135-2020" and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The grea<sup>t</sup> help from King Abdulaziz University's faculty members, including Radi A. Alsulami, Muhyaddin J. H. Rawa, Mashhour A. Alazwari, and Hatem F. Sindi are really appreciated.

**Conflicts of Interest:** The authors declare no conflict of interest.
